PHYS1160 Lesson 3 Notes

Lesson 3 – Where did it all begin?

Learning Outcomes

• Describe the history of the early Universe and the Big Bang.
• Outline the evidence that supports the Big Bang theory.
• Explain the cosmic microwave background and what it means.
• Outline the different possible shapes of the Universe.

3.1 The Big Bang

• Edwin Hubble discovered the Universe was expanding, which suggested it was smaller in the past, leading to the Big Bang theory.
• We can't "observe" the Big Bang directly because:
  • It occurred before stars and galaxies existed (no light).
  • The Universe is filled with radiation from when it was 380,000 years old (when it became "transparent to light").
• Computer modeling is used to study the Universe before this time.

3.2 The Big Bang Theory

• The Big Bang theory posits that everything began as a hot, dense collection of matter and radiation.
• The expansion of the Universe is analogous to the expansion of a gas (compression increases temperature).
• Modeling is used to determine the temperature of the early Universe.
• The graph in Figure 22.1 from The Cosmic Perspective shows how the temperature of the universe has cooled with time. The axis scales use powers of 10.
• Kinks in the graph at $10^{12}$ K and $10^9$ K represent when the universe became too cold to produce new protons and electrons, respectively.

3.3 The creation of particles

• Energy cannot be created nor destroyed, but it can change form; matter and energy can transform between these two states according to Einstein's equation: $E = mc^2$.
• Particle accelerators, like the Large Hadron Collider (LHC) at CERN, accelerate charged particles to near the speed of light and collide them.
• High-energy particle collisions produce new particles and annihilate others. For example, two gamma ray photons can collide to produce an electron (matter) and a positron (antimatter).
• Similar reactions occur for other particle-antiparticle pairs (protons/antiprotons, neutrons/antineutrons).
• Scientists can reproduce conditions from the first $10^{-10}$ seconds after the Big Bang in laboratories.

3.4 Fundamental forces

• The four fundamental forces are gravity, electromagnetism, the strong force, and the weak force.
• Gravity operates over the largest distances.
• The electromagnetic force is stronger than gravity and depends on the charges of particles. It governs chemical and biological reactions but is less significant over large distances due to neutral charges.
• The strong and weak forces operate over short distances (atomic nuclei).
• The strong force binds protons and neutrons in the nucleus, while the weak force plays a role in nuclear reactions (fission and fusion).
• During the earliest moments of the Universe, these forces may have been unified.
• Grand unified theories (GUTs) combine the strong, weak, and electromagnetic forces.

3.5 A timeline for the early life of the Universe

• The history of the Universe is divided into eras:
  • Planck Era ($10^{-43}$ s after the Big Bang):
    • Significant energy fluctuations.
    • Quantum mechanics and general relativity are not yet linked.
    • Gravity became distinct from other forces.
  • GUT era ($10^{-38}$ s after the Big Bang):
    • The GUT force split into the strong and electroweak forces.
    • Inflation (sudden expansion) occurred.
  • Electroweak era ($10^{-10}$ s after the Big Bang):
    • Electromagnetic and weak forces were combined (electroweak force).
    • Three forces existed: electroweak, strong, and gravitational.
    • The electroweak force theory predicted weak bosons (W and Z bosons) at temperatures above $10^{15}$ K, which has been confirmed by particle accelerators.
  • Particle era (1 millisecond after the Big Bang):
    • Matter and energy spontaneously exchanged forms.
    • Exotic particles were produced and annihilated.
    • Photons became the dominant form of energy.
    • Quarks combined to form protons and neutrons.
    • There was slightly more matter than antimatter.
    • Photons outnumber protons by roughly one billion to one.
  • Era of nucleosynthesis (5 minutes after the Big Bang):
    • Creation of nuclei (synthesis).
    • High-energy gamma rays broke apart heavier nuclei.
    • The mass content of the Universe was 75% hydrogen, 25% helium, and trace amounts of deuterium and lithium.
  • Era of nuclei (380,000 years after the Big Bang):
    • Hydrogen, helium, and trace elements existed as a plasma.
    • Atoms were fully ionized.
    • The era ended when temperatures reached 3,000 K.
    • Hydrogen, helium, and other elements captured electrons.
    • Photons could travel freely (cosmic microwave background).
  • Eras of atoms and galaxies (to present):
    • Density was not uniform, leading to protogalactic clouds.
    • Stars formed in clouds, creating galaxies.
    • Galaxies formed around 1 billion years after the Big Bang.

3.6 Evidence for the Big Bang

• Two major predictions:
  1. Radiation produced at the end of the era of nuclei should be observed.
  2. Around 25% of the initial hydrogen should have formed into helium.
• Cosmic Microwave Background Radiation:
  • Discovered by Arno Penzias and Robert Wilson in 1965.
  • The cosmic microwave background should fit the thermal radiation spectrum.
  • Radiation could travel freely when the temperature was around 3,000 K, with a peak at 1,000 nm.
  • The Universe has expanded by a factor of around 1,000, stretching the photons to 1 mm.
  • This corresponds to a temperature a few degrees K above absolute zero.
  • NASA's COBE satellite confirmed that the cosmic microwave background fits a thermal radiation spectrum perfectly at 2.73 K.
  • COBE, WMAP, and the Planck satellite mapped temperature fluctuations in the Universe.
  • Temperature fluctuations (a few parts in 100,000) indicate density fluctuations in the early Universe.
• Abundances of Elements:
  • Stars fuse hydrogen to create heavier elements.
  • The early Universe was predominantly hydrogen and helium.
  • No galaxy has a helium content less than 25%.
  • Scientists calculate that the predicted amount of helium at the end of the era of nucleosynthesis is 25%.
• Neutrons are slightly heavier than protons, requiring energy for conversion ($E = mc^2$).
• The proton to neutron ratio was initially 1:1 but favored protons as the temperature dropped.
• Protons and neutrons formed deuterium, which led to helium-4.
• Calculations show that the proton:neutron ratio should have been around 7:1, resulting in 25% helium.

3.7 Inflation

• Inflation is the rapid period of expansion the Universe underwent.
• Observed that inflation does not violate the theory of light speed because it is the expansion of space itself, not matter moving through space.
• Inflation explains:
  1. The origin of density fluctuations.
  2. The uniformity of the large-scale Universe.
  3. The flat geometry of the Universe.
• Density fluctuations:
  • Energy fields on the quantum scale fluctuate randomly.
  • Supported by Heisenberg's Uncertainty Principles (energy-time principle).
  • Quantum fluctuations expanded to large scales, becoming seeds for density irregularities.
• The large-scale Universe:
  • Separate regions have the same properties because they were in the same region before inflation.
• A flat Universe:
  • Matter curves spacetime (Einstein's general theory of relativity).
  • The shape of the Universe can be flat (critical), spherical (closed), or saddle (open).
  • The shape depends on the average density of matter and energy.
  • The Universe will be flat if the density equals the critical density.
  • Even if the overall shape is curved, the observable Universe will appear flat.
  • Surveys like WMAP and Planck have measured temperature fluctuations, matching predictions well.

3.8 Beyond a shadow of a doubt…

• It's hard to prove the Big Bang with absolute certainty.
• The Big Bang theory has no competing theory that explains the observable Universe so satisfactorily.
• Olbers’ paradox:
  • Why is the sky dark?
  • If the Universe were infinite, the entire night sky would be brightly lit because you would see a star in every possible direction.
  • The solutions are that the Universe is not infinite or changes over time.
  • The Universe changes over time, fitting the Big Bang theory.
  • We only see a finite number of stars because we are bound by the observable Universe.